On the Eight Dimensional Point Symmetries of Second Order Linear O.D.E's

Uchechukwu Opara

Abstract

The purpose of this paper is to review Sophus Lie's methods for differential equations, shedding light on the Lie point symmetries of generic linear second order ordinary differential equations (O.D.E's). As a matter of necessity in the overall review, there are important contrasts highlighted in derivations of the infinitesimal generators, with and without the prior application of point transformations.